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The Computer Journal 1971 14(4):422-425; doi:10.1093/comjnl/14.4.422
© 1971 by British Computer Society
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An algorithm with guaranteed convergence for finding a zero of a function

R. P. Brent *

Computer Science Department, Stanford University, Stanford, California, USA

An algorithm is presented for finding a zero of a function which changes sign in a given interval. The algorithm combines linear interpolation and inverse quadratic interpolation with bisection. Convergence is usually superlinear, and is never much slower than for bisection. ALGOL 60 procedures are given.

Received August 1970. Revised March 1971.

* Present address: P.O. Box 218, Yorktown Heights, New York 10598, USA.

§ Computer Science Department, Stanford University, Stanford, California 94305, USA


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